On the surjectivity of the map of spectra associated to a tensor‐triangulated functor
On the surjectivity of the map of spectra associated to a tensor‐triangulated functor
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关于与张量三角函子相关的光谱图的满射性
DOI：
10.1112/blms.12158
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发表时间：
2017
影响因子：
0.9
通讯作者：
Paul Balmer
中科院分区：
文献类型：
--
作者：
Paul Balmer
我们证明了关于张量三角函数 F 在张量三角谱上导出的映射 Spc(F) 的一些结果。首先，当且仅当 Spc(F) 在闭点上是满射时，F 是保守的。其次，如果 F 检测到态射的张量幂零性，则 Spc(F) 在整个谱上是满射的。事实上，Spc(F) 的满射性等价于 F 检测某类态射的幂零性，即那些在锥体上幂零的态射。
We prove a few results about the map Spc(F) induced on tensor‐triangular spectra by a tensor‐triangulated functor F . First, F is conservative if and only if Spc(F) is surjective on closed points. Second, if F detects tensor‐nilpotence of morphisms, then Spc(F) is surjective on the whole spectrum. In fact, surjectivity of Spc(F) is equivalent to F detecting the nilpotence of some class of morphisms, namely those morphisms which are nilpotent on their cone.